Monomer as a function of time

Polymerization reactions of multifunctional monomers such as those used in dental restorations occur in the high crosslinking regime where anomalous behavior is often observed, especially with respect to reaction kinetics. This behavior includes auto acceleration and autodeceleration [108-112], incomplete functional group conversion [108,109,113-116], a delay in volume shrinkage with respect to equilibrium [108, 117,118], and unequal functional group reactivity [119-121]. Figures 3 and 4 show a typical rate of polymerization for a multifunctional monomer as a function of time and conversion, respectively. Several distinctive features of the polymerization are apparent in the rate profiles. 

Static system, in which rate of reaction is determined by pressure drop of monomer as a function of time. 

More recently Saegusa et al. [120, 45] have developed a technique for the determination of the concentration of active centres, [P l, by terminating the polymerization with the sodium salt of phenol, Na OPh , and estimating the PhO-groups in the polymer spectrophoto-metrically. A closely related method has been used by Jaacks et al. [121] to estimate the concentration of tertiary ox onium ions in the polymerization of 1,3 dioxolan (Section 7.3). Saegusa has shown that the chromophore polymer—OPh has an absorption maximum, X iax 272 nm and an extinction coefficient, e, = 1.96 x 10 1 mole cm in methylene chloride. Consumption of monomer as a function of time was followed by a gravimetric method and the results interpreted [122] according to the kinetic scheme. 

Stable styrene miniemulsions were prepared by using alkyl methacrylates as the reactive cosurfactant. Data of monomer droplet size, creaming rate and phase separation of monomer as a function of time were used to evaluate the shelf-life of miniemulsions stabilised by sodium dodecyl sulphate in combination with various cosurfactants. 20 refs. 

The rate of copolymerization (f) of styrene with BMA was studied by using isothermal differential scanning calorimetry (DSQ. The conversion of monomer as a function of time can be obtained by integration of the DSC diagrams ... 

Figure 4.6 Variations of the average (a) size (b) angular momentum and (c) internal temperature of a 28-atom LJ cluster undergoing successive evaporation of monomers, as a function of time. The results of molecular dynamics (MD) simulations are compared with the predictions from phase space theory (PST) with calibrated rates and anharmonic state densities and also to approximate PST calculations in which the rates are either not calibrated or obtained from harmonic state densities.

Photoinitiated Cationic Polymerization. The cationic photopolymerization of the monomers synthesized above was studied using real-time infrared spectroscopy (RTIR).i This technique involves monitoring the decrease of an IR absorption characteristic of the functional group undergoing polymerization. In these studies, 2 mol % (4-decyloxyphenyl)phenyliodonium SbF was used as the photoinitiator. Figure 4 gives individual plots of the percent conversion of the various Tg monomers as a function of time at the optimum photoinitiator concentration for each of the monomers. The rate of photopolymerization of 1-propenyl ether functional monomer IX is the fastest followed by III, V and VI. 

Fig. 9.2. Photochemical model of the movement of monomers as a function of time [693]. (Reproduced with permission from American Institute of Physics, 1984.)...

VDF-HFP copolymerizations with in-line monitoring of the NIR and the MIR region provide access to conversion of both monomers as a function of time, as is illustrated in Figure 26(a). Since reacted monomer is converted into copolymer units, information on copolymer composition as a function of monomer feed composition is available. With one reactivity ratio value being below unity and the other one above unity, copolymer composition always differs from comonomer feed. 

We need to know the characteristic time beyond which we will cease to observe the global chain dynamics but only the center of mass motion. In answering such a question we need the relaxation time for a polymer chain which has been disturbed from its equilibrium configuration, and the mean square displacement of a labeled monomer as a function of time. 

The resolution of the system consisting of equations [5.34] to [5.37] will normally enable us to express the extinction speed of the monomer as a function of time through parameters v kp and k. Unfortunately, we obtain a mathematic system that is too comphcated to be solved and in addition a primordial reason is that the number of equations of the system varies with time (the problem s variable). We shall see in Chapter 7 how to bypass this difficulty. 

More recently, the reaction advancement of resole syntheses (pH = 8 and 60°C) was monitored using high-performance liquid chromatography (HPLC), 13C NMR, and chemical assays.55,56 The disappearance of phenol and the appearances of various hydroxymethyl-substituted phenolic monomers and dimers have been measured. By assessing the residual monomer as a function of reaction time, this work also demonstrated the unusually high reactivity of 2,6-dihydroxymethyl-phenol. The rate constants for phenolic monomers toward formaldehyde substitution have been measured (Table 7.6). 

Monomer concentration dynamics are presented in Figure 5. Additional observations for Run 5 are accurately correlated during the reactor startup and at final steady state. The observation at one residence time, Run 4, may be in error. The total cummu-lative, molar concentrations of macromolecules as a function of time are presented in Figure 6. The errors associated with this dependent variable are also evident during the steady state analysis of initiation... 

Simultaneous integration of these equations by numerical methods can provide the concentrations of A,B1,B2 and B3 as a function of time and the concentrations of o-methylol, p-methylol and methylene ether (note earlier definition) groups can be calculated as follows, where CONC is the initial monomer concentration. 

Marvel, Dec, and Cooke [J. Am. Chem. Soc., 62 (3499), 1940] have used optical rotation measurements to study the kinetics of the polymerization of certain optically active vinyl esters. The change in rotation during the polymerization may be used to determine the reaction order and reaction rate constant. The specific rotation angle in dioxane solution is a linear combination of the contributions of the monomer and of the polymerized mer units. The optical rotation due to each mer unit in the polymer chain is independent of the chain length. The following values of the optical rotation were recorded as a function of time for the polymerization of d-s-butyl a-chloroacrylate... 

To determine if this phenomenon is isolated to amorphous monomers, a liquid crystalline diacrylate (C6M) was polymerized in W7,W82 at temperatures corresponding to the two smectic phases as well as the isotropic phase. The polymerization rate for C6M is plotted as a function of time for representative temperatures in Figure 6. Again, the polymerization shows marked acceleration in the ordered smectic C phase and occurs much faster than the isotropic polymerization. As seen in the HDDA polymerizations, the smectic A rate also lies between the rates of the other two polymerization temperatures. 

Recently Biggs [74] has investigated the emulsion polymerisation of styrene using ultrasonic irradiation as the initiation source (i. e. in the absence of a chemical initiator). Similar to Lorimer and Mason using a thermally initiated system, Biggs found both a marked increase in monomer conversion rate as a function of time as the ultrasonic intensity was increased but remarkable constancy in the resultant latex particle... 

Chemical analysis of the unreacted monomer functional groups as a function of time is useful for step polymerizations. For example, polyesterification can be followed accurately by titration of the carboxyl group concentration with standard base or analysis of hydroxyl groups by reaction with acetic anhydride. The rate of chain polymerization of vinyl monomers can be followed by titration of the unreacted double bonds with bromine. 

Equation 5 expresses the variation in the concentration of monomer A in the feed stream entering the reactor as a function of time. Since this variation is a power function of time, the process has been named "power feed."... 

Only two spectroscopic studies on sulfur vulcanisation of EPDM by Fujimoto and coworkers are available [73-74], Using attenuated total reflectance (ATR) IR spectroscopy they showed that during sulfur/TMTD/MBT/ZnO/stearic acid vulcanization, the C=C bands at 3035, 966 and 870 cm 1 of the residual unsaturations of the EPDM third monomers, DCPD, 1,4-hexadiene (HD) and 5-methylidene-2-norbornene (MNB), respectively, decreased in intensity as a function of time at 140 and 150 °C. The relative decrease in intensity was shown to correlate with the increase in crosslink density. In Sections 6.2.2.2 and 6.2.2.3 it will be shown that this decrease of intensity should not be interpreted as a loss of unsaturation during sulfur vulcanisation of EPDM. 

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